Pollinator Indicators

1. Introduction

We aim to model the diversity of pollinators in Norway given their know interaction with some plant species. From the estimated diversity across the nation, we intend to look at the estimates in the ASO Data meadows by using their values as the reference values. To achieve this, we do the following:

1. obtain data from the Global Biodiversity Infrastructure Facility (GBIF ) for bumblebees, butterflies and bees.
1. fit an integrated species distribution model (ISDM) to the data to obtain the distribution of pollinators
1. obtain a web plot interaction matrix of the pollinator and plant species
1. get data on the plant species within the interaction matrix from GBIF
1. fit an ISDM data obtained in step (d) to estimate their respective species occurrence probability
1. estimate the alpha diversity index of the pollinators across Norway using the results obtained in (b), (c) and (d).

Figure 1: Flowchart of the modelling framework used in estimating the pollinator potential in this project. The modelling start with A) obtaining bees, bumblebees and hoverflies data from GBIF and fitting ISDMs to the pollinator data, then B) obtaining data on some selected plant species from GBIF and fitting ISDMs to the plant data, C) constructing the interraction between the plant and pollinators (from a given data) and D) estimating the alpha diversity indices. The covariate used to fit the ISDMs are presented in Table 7. The dataset and covariates are enclosed in dashed green-colored rectangular regions.

2. About the underlying data

The pollinator (GBIF.Org User 2024a) and plant species (GBIF.Org User 2024b) data used to fit the ISDMs were obtained from GBIF. The data was downloaded via the R-package rgbif (Chamberlain et al. 2024), and extract the associated metadata using the same R-package. We downloaded GBIF data contains \(26\) datasets and \(30\) datasets with records on pollinators and plants respectively. We present a summary of the datasets downloaded for the pollinator and plant species respectively in Table 5 and Table 6 respectively.

From the metadata, we ascertain the type of each dataset: either presence-only, presence-absence or count data. We merge all the presence-only data into one dataset (which we call mergedDatasetPO), but we do not merge the rest of the datasets. This is because the presence-absence data (procesed from sampling event protocols) have different sampling protocols, and we would like to preserve their unique attributes. A summary of the formatted dataset used to fit the ISDMs are presented in Table 2 and Table 3.

Table 2: Number of pollinator occurrences from the formatted datasets obtained from GBIF. All presence-only datasets are merged into one dataset (mergedDataset).

Dataset name	No. of bees occurrences	No. of butterflies occurrences	No. of hoverflies occurrences
mergedDatasetPO	22316	61009	17555
National insect monitoring in Norway	182	157	241
Saproxylic insects caught in window traps and hatched from polypores in small and large old forests in southern Norway	5	5	5
Solitary bees collected in a large-scale field experiment in power line clearings, southeast Norway	391	0	0
Freshwater benthic invertebrates ecological collection NTNU University Museum	3560	3569	5433
Bumble bees collected in a large-scale field experiment in power line clearings, southeast Norway	78	0	0
Bumblebees and butterflies in Norway	5687	5192	0
Freshwater pelagic invertebrates ecological collection NTNU University Museum	1573	1573	1574

Table 3: Number of plant occurrences from the formatted datasets obtained from GBIF. All presence-only datasets are merged into one dataset (mergedDataset).

Species	mergedDatasetPO	Monitoring data of natural and man-made semi-natural meadows in and around Oslo, Norway 2018-2021	Vegetation data with and without experimental warming, alpine Finse 2000, 2004, 2011	Effects of vegetation clearing on vascular plants in power line clearings southeast Norway	Vascular plants in power line clearings and the nearby forest, southeast Norway	Overvåking av semi-naturlig eng (ASO)
Ajuga pyramidalis	4003	22	720	1533	599	153
Astragalus alpinus	1851	22	720	1533	599	153
Campanula rotundifolia	11703	22	720	1533	599	153
Carum carvi	2584	22	720	1533	599	153
Filipendula ulmaria	15967	22	720	1533	599	153
Galium album	3624	22	720	1533	599	153
Galium aparine	1722	22	720	1533	599	153
Galium boreale	7360	22	720	1533	599	153
Galium elongatum	1399	22	720	1533	599	153
Galium palustre	2180	22	720	1533	599	153
Galium saxatile	1299	22	720	1533	599	153
Galium uliginosum	1761	22	720	1533	599	153
Galium verum	3276	22	720	1533	599	153
Geranium robertianum	5497	22	720	1533	599	153
Geranium sylvaticum	13861	22	720	1533	599	153
Gymnadenia conopsea	3179	22	720	1533	599	153
Hieracium murorum	20	22	720	1533	599	153
Hieracium umbellatum	3663	22	720	1533	599	153
Hieracium vulgatum	26	22	720	1533	599	153
Hypochaeris radicata	1287	22	720	1533	599	153
Knautia arvensis	6030	22	720	1533	599	153
Lathyrus linifolius	6118	22	720	1533	599	153
Lathyrus pratensis	5458	22	720	1533	599	153
Lathyrus vernus	2013	22	720	1533	599	153
Leucanthemum vulgare	9160	22	720	1533	599	153
Lotus corniculatus	11190	22	720	1533	599	153
Nardus stricta	5966	22	720	1533	599	153
Origanum vulgare	2178	22	720	1533	599	153
Plantago lanceolata	5091	22	720	1533	599	153
Plantago major	6525	22	720	1533	599	153
Plantago media	2045	22	720	1533	599	153
Silene dioica	6888	22	720	1533	599	153
Silene vulgaris	3343	22	720	1533	599	153
Stellaria graminea	7784	22	720	1533	599	153
Stellaria media	3723	22	720	1533	599	153
Stellaria nemorum	3694	22	720	1533	599	153
Trifolium medium	4394	22	720	1533	599	153
Trifolium pratense	11519	22	720	1533	599	153
Trifolium repens	10479	22	720	1533	599	153
Trollius europaeus	2856	22	720	1533	599	153
Valeriana sambucifolia	106	22	720	1533	599	153
Veronica alpina	403	22	720	1533	599	153
Veronica chamaedrys	8302	22	720	1533	599	153
Veronica officinalis	10738	22	720	1533	599	153
Veronica serpyllifolia	711	22	720	1533	599	153
Vicia cracca	9257	22	720	1533	599	153
Vicia sepium	5705	22	720	1533	599	153
Vicia sylvatica	1969	22	720	1533	599	153
Viola biflora	2990	22	720	1533	599	153
Viola canina	3163	22	720	1533	599	153
Viola epipsila	423	22	720	1533	599	153
Viola palustris	7853	22	720	1533	599	153
Viola riviniana	8650	22	720	1533	599	153
Viola tricolor	3667	22	720	1533	599	153

2.1 Spatial and temporal resolution

Both pollinator and plant data obtained on a National scale (entire Norway) observed within \(2010\) to \(2024\). We present an illustration of the spatial distribution of the pollinator in the merged Presence-only and National insect monitoring in Norway datasets across the study region in Figure 2.

Figure 2: Distribution of bees, butterflies and hoverfies in the merged Presence-only and National insect monitoring in Norway datasets. The merged Presence-only dataset is colored by the taxon, and the National insect monitoring dataset is colored by the presence (1) or absence (0) value.

Iintend to keep either the table or the figures in the final document, depending on what is needed for the report.

2.2 Original units

The original unit of the each dataset obtained from GBIF for the pollinators and plants are provided in Table 5 and Table 6 respectively. The dataset are either presence-only and presence-absence.

2.3 Additional comments about the dataset

3. Indicator properties

Anders will help with this

3.1. ECT

3.2. Ecosystem condition characteristic

3.3. Other standards

3.4. Collinearities with other indicators

4. Reference condition and values

4. 1. Reference condition

4. 2. Reference values

4.2.1 Minimum and maximum values

Reference values for diversity indices at the ASO data meadows.

Shannon diversity indices at ASO data locations.

4.2.2. Threshold value for defining good ecological condition (if relevant)

4.2.3. Spatial resolution and validity

5. Uncertainties

6. References

7. Datasets

Here, we describe each of the dataset used for the modelling. We refer the readers to the dataset description provided on the GBIF website.

Table 4: Datasets obtained on selected plant species from GBIF, the type of dataset, total number of occurrence records in each dataset and its percentage in the total number of occurrence records. The dataset with type sampling_event is treated as presence-absence, occurrence as presence-only and insectMonitoring as count data.

Dataset	Link to description
Bumble bees collected in a large-scale field experiment in power line clearings, southeast Norway	https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee
Bumblebees and butterflies in Norway	https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee
Ecofact	https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee
Entomological collections, UiB	[link](https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee)
Entomology collection, UiT Tromsø Museum	NA
Entomology, Oslo (O) UiO	NA
Freshwater benthic invertebrates ecological collection NTNU University Museum	NA
Freshwater pelagic invertebrates ecological collection NTNU University Museum	NA
Insect collection, UiT, University Museum (TSZ). Insect labeling project and PhD-duty-work	NA
Insects of the Forest-Tundra Ecotone (ForTunE)	NA
Invertebrate collections, UiB	NA
Jordal	NA
Lepidoptera collection, South Norway	NA
Mapping and monitoring of the Glanville fritillary Melitaea cinxia	NA
NINA insect database	NA
NORSC - Sciaroidea, UiT Tromsø Museum	NA
National insect monitoring in Norway	https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee
Norwegian Biodiversity Information Centre - Other datasets	NA
Norwegian Species Observation Service	NA
Observation.org, Nature data from around the World	NA
Occurrence data from various smaller projects in Norway	NA
Saproxylic insects caught in window traps and hatched from polypores in small and large old forests in southern Norway	https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee
Solitary bees collected in a large-scale field experiment in power line clearings, southeast Norway	NA
Terrestrial and limnic invertebrates systematic collection, NTNU University Museum	NA
iNaturalist Research-grade Observations	NA
naturgucker	NA

Here, intend to link all the datasets to their correct version on the GBIF repository.

7.1 Pollinator datasets

Table 5: Datasets obtained on pollinators from GBIF, the type of dataset, total number of occurrence records in each dataset and its percentage in the total number of occurrence records. The dataset with type sampling_event is treated as presence-absence, occurrence as presence-only and insectMonitoring as count data.

Dataset name	Data type	No. of observations	Percent
Bumble bees collected in a large-scale field experiment in power line clearings, southeast Norway	SAMPLING_EVENT	5016	0.28
Bumblebees and butterflies in Norway	SAMPLING_EVENT	31112	1.75
Ecofact	OCCURRENCE	2	0.00
Entomological collections, UiB	OCCURRENCE	2757	0.16
Entomology collection, UiT Tromsø Museum	OCCURRENCE	2	0.00
Entomology, Oslo (O) UiO	OCCURRENCE	63124	3.56
Freshwater benthic invertebrates ecological collection NTNU University Museum	SAMPLING_EVENT	11559	0.65
Freshwater pelagic invertebrates ecological collection NTNU University Museum	SAMPLING_EVENT	17	0.00
Insect collection, UiT, University Museum (TSZ). Insect labeling project and PhD-duty-work	OCCURRENCE	2048	0.12
Insects of the Forest-Tundra Ecotone (ForTunE)	OCCURRENCE	216	0.01
Invertebrate collections, UiB	OCCURRENCE	14	0.00
Jordal	OCCURRENCE	48	0.00
Lepidoptera collection, South Norway	OCCURRENCE	613	0.03
Mapping and monitoring of the Glanville fritillary Melitaea cinxia	OCCURRENCE	785	0.04
NINA insect database	OCCURRENCE	21342	1.20
NORSC - Sciaroidea, UiT Tromsø Museum	OCCURRENCE	6886	0.39
National insect monitoring in Norway	insectMonitoring	610146	34.41
Norwegian Biodiversity Information Centre - Other datasets	OCCURRENCE	21	0.00
Norwegian Species Observation Service	OCCURRENCE	971031	54.75
Observation.org, Nature data from around the World	OCCURRENCE	4636	0.26
Occurrence data from various smaller projects in Norway	OCCURRENCE	7	0.00
Saproxylic insects caught in window traps and hatched from polypores in small and large old forests in southern Norway	SAMPLING_EVENT	122	0.01
Solitary bees collected in a large-scale field experiment in power line clearings, southeast Norway	SAMPLING_EVENT	2699	0.15
Terrestrial and limnic invertebrates systematic collection, NTNU University Museum	OCCURRENCE	32654	1.84
iNaturalist Research-grade Observations	OCCURRENCE	6456	0.36
naturgucker	OCCURRENCE	99	0.01

Out of the 26 datasets obtained from GBIF, over half of the total occurrence reports for the pollinators were from the Norwegian species Observation Service, a third of the total occurrence report were from the National insect monitoring in Norway, and the other 24 datasets cover 22 percent of the total pollinator occurrences.

Figure 3: Distribution of bees, butterflies and hoverfies caight in window traps and those collected in large-scale field experiment in power line clearings. The observations are colored by the presence (1) or absence (0) value.

After processing the data, it is important that we filter only the bees from the following datasets: Solitary bees collected in a large-scale field experiment in power line clearings (southeast Norway), Bumble bees collected in a large-scale field experiment in power line clearings (southeast Norway), as can be seen in Figure 3 and Figure 4.

Figure 4: Distribution of bees, butterflies and hoverfies NTNU university Museum collection and large scale field experiment in Norway. The observations are colored by the presence (1) or absence (0) value.

We also filter out bees and butterflies datasets from the Bumblebees and butterflies in Norway dataset, displayed in Figure 5.

Figure 5: Distribution of bees, butterflies and hoverfies in the Bumblebees and butterflies in Norway and freshwater pelagic invertebrates ecological collection from the NTNU University Museum datasets. The observations are colored by the presence (1) or absence (0) value.

7.2. Plant datasets

From our query for datasets from GBIF, we got a total of 30 datasets which we used to fit the ISDM for the plants. Out of these occurrence records, about 86 percent of these records were from the Norwegian species Observation Service.

Table 6: Datasets obtained on selected plant species from GBIF, the type of dataset, total number of occurrence records in each dataset and its percentage in the total number of occurrence records. The dataset with type sampling_event is treated as presence-absence, occurrence as presence-only and insectMonitoring as count data.

Dataset name	Data type	No. of observations	Percent
ARKO strandeng	OCCURRENCE	274	0.09
Ecofact	OCCURRENCE	51	0.02
Effects of vegetation clearing on vascular plants in power line clearings southeast Norway	SAMPLING_EVENT	779	0.24
Jordal	OCCURRENCE	5434	1.70
Monitoring data of natural and man-made semi-natural meadows in and around Oslo, Norway 2018-2021	SAMPLING_EVENT	2310	0.72
Norwegian Species Observation Service	OCCURRENCE	288837	90.51
Observation.org, Nature data from around the World	OCCURRENCE	2993	0.94
Occurrence data from various smaller projects in Norway	OCCURRENCE	775	0.24
Overvåking av semi-naturlig eng (ASO)	SAMPLING_EVENT	1606	0.50
Overvåking av åpen grunnlendt kalkmark i Oslofjordområdet	OCCURRENCE	1781	0.56
Pl@ntNet automatically identified occurrences	OCCURRENCE	3265	1.02
Pl@ntNet observations	OCCURRENCE	443	0.14
Stabbetorp - Floristiske registreringer 2016	OCCURRENCE	1209	0.38
Vascular Plant Herbarium, Oslo (O) UiO	OCCURRENCE	1006	0.32
Vascular Plant Herbarium, UiB	OCCURRENCE	45	0.01
Vascular Plants, Observations, Oslo (O)	OCCURRENCE	192	0.06
Vascular plant herbarium (KMN) UiA	OCCURRENCE	299	0.09
Vascular plant herbarium TRH, NTNU University Museum	OCCURRENCE	659	0.21
Vascular plant herbarium, The Arctic University Museum of Norway (TROM)	OCCURRENCE	208	0.07
Vascular plants in power line clearings and the nearby forest, southeast Norway	SAMPLING_EVENT	269	0.08
Vegetation data with and without experimental warming, alpine Finse 2000, 2004, 2011	SAMPLING_EVENT	148	0.05
iNaturalist Research-grade Observations	OCCURRENCE	6509	2.04
naturgucker	OCCURRENCE	28	0.01

Figure 6: Distribution of plant species in the merged presence-only dataset.

Figure 7: Distribution of plant species in the ASO data. The observations are colored by the presence (1) or absence (0) value.

7.3. Covariates

We used several covariates to fit both the pollinator and plant ISDMs. The names of the covariates, their description and source are presented in Table 7. Additionally, we include the indication of whether the covariate is a habitat, trait or climatic variables as well as which of the ISDMs it was used to fit in Table 7. The rasters of the covariates are on \(1\) km resolution.

Table 7: Description of covariates used to fit the integrated species distribution models and the source the covariates were retrieved from. The table indicated what type of covariate (habitat, trait and climatic) and which of the distributions it was used for (pollinator and/or plant) ISDM

Name	Description	Source	Habitat/ Trait/ Climatic	Disribution
bio1	Annual temperature	geodata R-package	Climatic	Pollinator, Plant
cellID	1 km grid cell created from the bio1 raster	NA	Trait	NA
Latitude	Latitudinal gradient extracted from the bio1 raster	NA	Trait	Pollinator
mBio1	Mean pollinator annual temperature per each pollinator species	NA	Trait	Pollinator
sdBio1	Standard deviation of pollinator annual temperature per each pollinator species	NA	Trait	Pollinator
mLat	Mean pollinator latitude per each pollinator species	NA	Trait	Pollinator
sdLat	Standard deviation of pollinator latitude per each pollinator species	NA	Trait	Pollinator
RegCom	NA	NA	Trait	Pollinator
landCover	Land cover raster	NA	Habitat	Pollinator, Plant
soilPh	NA	NA	Habitat	Plant
soilCoarseFraction	NA	NA	Habitat	Plant
soilOrganicCarbon	NA	NA	Habitat	Plant
soilMoisture	NA	NA	Climatic	Plant
bio1sq	Square of the annual temperature	NA	Climatic	Pollinator
bmInt	Interraction between the annual temperature and mean pollinator annual temperature per each pollinator species	NA	Climatic	Pollinator
bmIntsq	square of interraction between the annual temperature and mean pollinator annual temperature per each pollinator species	NA	Climatic	Polinator

We present the distribution of the covariates described in Table 7 here in Figure 8.

Figure 8: Covariates used to fit the ISDM. The resolution of the covariates are on a 1 km resolution.

8. Spatial units

9. Analyses

We fitted an ISDM using the point process framework [REF] to the merged pollinator presence-only (PO) and presence-absence (PA) datasets. ISDMs are various observation models that are linked together by a shared ecological process.

9.1. General overview of ISDMs

In this subsection, we present an overview of the ISDMs for general understanding of this document. For further details on ISDM, refer to Isaac et al. (2020), Dorazio (2014) and Fithian et al. (2015). The models are described using the point process framework as described in Adjei et al. (2023). Additionally, we present the description of these models under the assumption that we are fitting a multi-species ISDM.

We model the presence-only data as a Poisson point process model (Illian et al. 2008) with mean intensity \(\lambda_i(s)\) for each species \(i = 1, \ldots, S\), where \(S\) is the number of species.This mean intensity modelled as: \[\begin{equation} \label{eq:int} \ln(\lambda_i(s)) = \beta_{0i} + \beta_{ji} X_j(s) + \omega_i(s) + \eta(s), \end{equation}\] where \(\beta_{0i}\) is the species-specific intercept, \(\beta_{ji}\) is the species-specific effect of covariate \(j\), \(X_j(s)\) is the \(j^{th}\) covariate field, \(\omega_i(s)\) is the species-specific spatial autocorrelation field and \(\eta(s)\) is the bias field. \(\omega_i(s)\) and \(\eta(s)\) are modeled as zero mean Gaussian random field (i.e. \(\omega_i(s) \sim N(0, \Sigma)\), where \(\Sigma\) is a Mat’ern covariance matrix with variance \(\sigma_{i}^2\) and range \(\kappa_i\) and \(\eta(s) \sim N(0, \Sigma_\eta)\), where \(\Sigma_\eta\) is a Mat’ern covariance matrix with variance \(\tau^2\) and range \(\kappa_\eta\)).

We model the presence-absence data with a logistic regression model. Let \(y_i(s)\) be a binary value at location \(s\) with \(0\) indicating absence of species \(i\) and \(1\) indicating presence of species \(i\). Then \(y_i(s) \sim \text{Bernoulli}(\Psi_i(s))\) with: \[ cloglog(\Psi_i(s)) = \beta_{0i} + \beta_{ji} X_j(s) + \omega_i(s) \] where the parameters \(\beta_0\), \(\beta_1\) and \(\omega\) are defined in equation \(\ref{eq:int}\).

All the ISDMs were fitted using the R-package PointedSDMs (Mostert and O’Hara 2023).

9.2. ISDM for pollinators

Using the model framework defined above, we fitted the ISDM to the pollinator dataset obtained from GBIF. Due to memory available, we fit the ISDM seperately for each pollinator.

Code

# Load data and covariates
source("pipeline/dataImport/importPollinatorFromGBIF.R")
source("pipeline/dataImport/environmentalDataImport.R")

# Set the model
model <- PointedSDMs::startSpecies(PointsBeesAndButterfliesAndHoverflies, # list of pollinator dataset (containing both mergedDatasetPA and mergedDatasetPO) 
                                   Boundary = regionGeometry, # boundary of the study
                                   Projection = newCrs, # projection
                                   Mesh = meshForProject, #mesh used for the model
                                  speciesEnvironment = TRUE, # Should we have pollinator specific covariate effect
                                  speciesIntercept = TRUE, # TRUE treats the intercept as a random effect, instead of constrained as with a fixed effect 
                                  pointsIntercept = FALSE, #should we include intercept for each dataset
                                  pointCovariates = FALSE, #do we have covariates for the presence-only data
                                   responsePA = 'individualCount', # column name of the response values for presence-absence data
                                  # trialsPA = 'trials',
                                   spatialCovariates = envCovsForModel, # raster of spatia covariates
                                   speciesName = 'Taxon', # Names of the species in the datasets
                                   pointsSpatial = NULL, # Do not include a dataset spatial field
                                   speciesSpatial = "replicate")   # unique spatial field per species, but they share the same hyperparameters.

# Add second bias field for PO data
model$addBias(datasetNames = 'mergedDatasetPO')

9.2.1 Priors

We assume the following priors for the pollinator ISDM:

The probability that the standard deviation of the pollinator spatial field is greater than \(1\) is \(0.1\) (i.e. \(P(\sigma_\omega > 0.1) = 0.1\)).
The probability that the standard deviation of the bias field is greater than \(1\) is \(0.1\) (i.e. \(P(\sigma_\eta > 0.1) = 0.1\))
The probability that the spatial range of the pollinator spatial field is less than \(15\)km is \(0.1\) (i.e \(P(\kappa_\omega < 15) = 0.1\))
The probability that the spatial range of the pollinator spatial field is less than \(15\)km is \(0.1\) (i.e. \(P(\kappa_\eta < 15) = 0.1\))
effects of continuous covariates (all covariates except land cover) and the intercept for each pollinator is assumed to be from a Normal distribution with mean \(0\) and variance of \(1\).

Code

# hyper parameters of the spatial field (shared across species)
model$specifySpatial(Species = TRUE,  # define same prior for the all species
                     prior.sigma = c(1, 0.1),  # SD of field variation; 
                     prior.range = c(15, 0.1))  # range of spatial correlation; 


model$specifySpatial(Bias = TRUE, # Change the prior
                                 prior.sigma = c(1, 0.1),
                                 prior.range = c(15, 0.1))

model$specifyRandom(
  # precision parameter on how much each species' spatial field (how much they can deviate from the shared ___)
  speciesGroup = list(model = "iid", 
                      hyper = list(prec = list(prior = "pc.prec",
                                               param = c(0.1, 0.1)))), 
  # precision parameter on the baseline species occurrence rate
  speciesIntercepts = list(prior = 'pc.prec',
                           param = c(0.1, 0.1)))  

# Specify priors for covariate effects (continuous)
covariatesToAddEffects <- c("bio1", "bio.sq", "bmInt", "RegCom", "mBio1", "sdBio1", "sdmInt", "Latitude", "mLat", "sdLat", "mlatInt")
for(covs in covariatesToAddEffects){
  model$priorsFixed(Effect = covs,
                    mean.linear = 0,
                    prec.linear = 1)
}

9.2.2 Fit model and make predictions

We fit the model and make predictions of the pollinator intensity within the study region. We fit the model by using the adaptive strategy of the composite design integration strategy in INLA (Rue, Martino, and Chopin 2009).

Code

modelOptions <- list(num.threads = 4,
                     control.inla = list(int.strategy = 'ccd', 
                                         diagonal = 0.001, 
                                         cmin = 0, 
                                         strategy = "adaptive",
                                         control.vb= list(enable = FALSE)), 
                     verbose = FALSE, 
                     safe = TRUE, 
                     inla.mode = "experimental")

modelRun <- PointedSDMs::fitISDM(data = model, 
                            options = modelOptions)
  
  # predictions for this model
  individualDatasetPreds <- predict(modelRun,
          data = ppxl,
          predictor = TRUE,
          n.samples = 100)

9.2.3 Pollinator ISDM validation

We perform a five-fold cross validation to assess the trait effect on the pollinator distribution across the study region.

9.3. ISDM for plant species

Modelling all the \(54\) species required memoey allocations we did not have, so we split the species into groups with \(10\) species in each group. We fitted independent ISDMs for each of the groups.

Code

# PointedSDMs takes a longer time to fit for many species
# The trick to to break it into smaller groups
# The split will be done by the number of present speccies in each location
# I will split it nGroups time
sortedSpecies <- table(asoDatasf$acceptedScientificName)%>%
  as.data.frame()%>%
  dplyr::arrange(desc(Freq))%>%
  select(Var1)%>%
  c()

# Set the number of groups
nGroups <- 10

#split the species into groups of 10 species in each
plantSpeciesGroup <- split(sortedSpecies$Var1, 
                           seq(1, 
                               ceiling(length(sortedSpecies$Var1)/nGroups)))

Similar to the model the pollinator ISDM, we fitted an ISDM to the \(54\) plant species. The ISDM has species-specific intercept, covariate effect and spatial field (but all the species share the same hyperparameters). We also added a spatial bias field to the observation model for the presence-only dataset.

Code

speciesModelShared <- PointedSDMs::startSpecies(formatPlantData,
                                                Boundary = regionGeometry, 
                                   Projection = newCrs, 
                                   Mesh = meshForProject,
                                   responsePA = 'individualCount',
                                   speciesEnvironment = TRUE,
                                   speciesIntercept = TRUE,
                                   spatialCovariates = envCovsForPlantSpeciesModel, 
                                   speciesName = 'simpleScientificName',
                                   pointsIntercept = FALSE,
                                   pointsSpatial = NULL, # Do not include a dataset spatial field
                                   speciesSpatial = "replicate")  

# Add bias spatial field for the PO dataset
speciesModelShared$addBias(datasetNames = 'mergedPlantsPO')

9.3.1 Priors

We assume the following priors for the pollinator ISDM:

The probability that the standard deviation of the pollinator spatial field is greater than \(0.1\) is \(0.1\) (i.e. \(P(\sigma_\omega > 0.1) = 0.1\)).
The probability that the standard deviation of the bias field is greater than \(0.1\) is \(0.1\) (i.e. \(P(\sigma_\eta > 0.1) = 0.1\))
The probability that the spatial range of the pollinator spatial field is greater than \(50\) is \(0.1\) (i.e \(P(\kappa_\omega < 50) = 0.1\))
The probability that the spatial range of the pollinator spatial field is greater than \(50\) is \(0.1\) (i.e. \(P(\kappa_\eta < 50) = 0.1\))

Code

# hyper parameters of the spatial field (shared across species)
speciesModelShared$specifySpatial(Species = TRUE,  # define same prior for the all species
                     prior.sigma = c(1, 0.1),  
                     prior.range = c(5, 0.1))  


speciesModelShared$specifySpatial(Bias = TRUE, # Change the prior
                     prior.sigma = c(0.6, 0.1),
                     prior.range = c(5, 0.1))

# prior for random effects (mesh nodes of spatial field and species intercepts)
speciesModelShared$specifyRandom(
  # precision parameter on how much each species' spatial field (how much they can deviate from the shared ___)
  speciesGroup = list(model = "iid", 
                      hyper = list(prec = list(prior = "pc.prec",
                                               param = c(0.1, 0.1)))),  
  # precision parameter on the baseline species occurrence rate
  speciesIntercepts = list(prior = 'pc.prec',
                           param = c(0.1, 0.1)))

9.3.2 Model fitting and predictions

We fit the model by using the adaptive strategy of the composite design integration strategy in INLA.

Code

# specify the model options for INLA
modelOptions <- list(num.threads = 4,
                     control.inla = list(int.strategy = 'ccd', 
                                         diagonal = 0.001, 
                                         cmin = 0, 
                                         strategy = "adaptive",
                                         control.vb= list(enable = FALSE)), 
                     verbose = FALSE, 
                     safe = TRUE, 
                     inla.mode = "experimental")

# Species-specific spatial effects model
speciesSharedEst <- PointedSDMs::fitISDM(data = speciesModelShared, 
                            options = modelOptions)

# I proceed with the prediction of occupancy probabilities
# over the entire region
individualDatasetPreds <- predict(speciesSharedEst,
                                  data = ppxl,
                                  predictor = TRUE,
                                  n.samples = 500)

9.4 Species Interractions

Code

  load("../data/webPlot.RData")
  #interractionMatrix <- readr::read_csv(paste0(dataFolder,"/interractionsData/interractionMatrix.csv"))
  
    bipartite::plotweb(WebReady[[1]])

Webplot of plant species and pollinator interractions.

9.5. Diversity Indices

To define the diversity of the pollinators, we estimate the pollinator intensity given their interaction with the plants species within the location \(s\). This is estimated as: \[\begin{equation} \begin{split} \text{Intensity for intensity} &\propto \text{Estimated pollinator intensity} \times \text{Interraction weight} \times \text{plant species occurrence probability}\\ \implies \lambda^{\star}_i(s) &= \frac{\lambda_i(s) \times w_{ik} \times \Psi_k(s)}{\sum_k \lambda_i(s) \times w_k \times \Psi_k(s)}, \end{split} \end{equation}\] where \(w_k\) is the weight of the interaction between pollinator \(i\) and plant species \(k\), \(\Psi_k(s)\) is the occurrence probability of plant species \(k\) and \(\lambda_i(s)\) is the intensity of pollinator \(i\).

We estimated the Hill’s diversity indices for the pollinators. The Hill’s diversity indices are defined as: \[ H(s) = r_i(s) \times log(r_i(s)); \] where \(r_i(s) = \frac{\lambda^{\star}_i(s)}{\sum_{i} \lambda^{\star}_i(s)}\).

10. Results

10.1. Distribution of pollinators accross Norway

We present the predictions of log-intensity of the pollinators in Figure 9 and its standard error in Figure 10. The log-intensity for the three pollinators: bees, butterflies and hoverflies are similar with standard error close to \(0\). This result can be seen as a direct consequence of the estimates of climatic and trait variables on the pollinator distribution (Figure 11 and Figure 12).

Figure 9: Log intensity of pollinators (bees, butterfliesand hoverflies) across the study region from the fitted integrated species distribution model.

Figure 10: Standard error of the log-intensity of pollinators (bees, butterfliesand hoverflies) across the study region from the fitted integrated species distribution model.

The effects of traits and climatic variables on the pollinator distribution in Figure 11. There is a negative latitudinal effect on bees and butterflies, but a positive effect on hoverflies. However, there is a positive effect of annual temperature on butterflies and bees, but a negative effect on hoverflies. There is an insignificant trait effects on the hoverflies distribution as their credible interval of these covariates includes \(0\). The contrast of this statement is true for the bees and butterflies distribution.

Figure 11: Effects of traits and climatic variables on the pollinator distribution.

In contrast to the trait and climatic variables, there seems to be … (Figure 12).

Figure 12: Plant species land cover effects.

Figure 14: Diversity of pollinators across Norway.

11. Export file

12. References

Adjei, Peprah Kwaku, Philip Mostert, Jorge Sicacha Parada, Emma Skarstein, and Robert B O’Hara. 2023. “The Point Process Framework for Integrated Modelling of Biodiversity Data.” arXiv e-Prints, arXiv–2311.

Chamberlain, Scott, Vijay Barve, Dan Mcglinn, Damiano Oldoni, Peter Desmet, Laurens Geffert, and Karthik Ram. 2024. Rgbif: Interface to the Global Biodiversity Information Facility API. https://CRAN.R-project.org/package=rgbif.

Dorazio, Robert M. 2014. “Accounting for Imperfect Detection and Survey Bias in Statistical Analysis of Presence-Only Data.” Global Ecology and Biogeography 23 (12): 1472–84. https://doi.org/10.1111/geb.12216.

Fithian, William, Jane Elith, Trevor Hastie, and David A. Keith. 2015. “Bias Correction in Species Distribution Models: Pooling Survey and Collection Data for Multiple Species.” Methods in Ecology and Evolution 6 (4): 424–38. https://doi.org/10.1111/2041-210X.12242.

GBIF.Org User. 2024a. “Occurrence Download.” The Global Biodiversity Information Facility. https://doi.org/10.15468/DL.ZSEX2M.

———. 2024b. “Occurrence Download.” The Global Biodiversity Information Facility. https://doi.org/10.15468/DL.AWRNR2.

Illian, Janine, Antti Penttinen, Helga Stoyan, and Dietrich Stoyan. 2008. Statistical Analysis and Modelling of Spatial Point Patterns. John Wiley & Sons.

Isaac, Nick JB, Marta A Jarzyna, Petr Keil, Lea I Dambly, Philipp H Boersch-Supan, Ella Browning, Stephen N Freeman, et al. 2020. “Data Integration for Large-Scale Models of Species Distributions.” Trends in Ecology & Evolution 35 (1): 56–67. https://doi.org/10.1016/j.tree.2019.08.006.

Mostert, Philip S, and Robert B O’Hara. 2023. “PointedSDMs: An r Package to Help Facilitate the Construction of Integrated Species Distribution Models.” Methods in Ecology and Evolution 14 (5): 1200–1207.

Rue, Håvard, Sara Martino, and Nicholas Chopin. 2009. “Approximate Bayesian Inference for Latent Gaussian Models Using Integrated Nested Laplace Approximations (with Discussion).” Journal of the Royal Statistical Society B 71: 319–92.

Indicator ID	NA
Indicator Name	Pollinator Indicators
Country	Norway
Continent	Europe
Ecosystem Condition Typology Class	NA
Realm	Terrestrial (T)
Biome	NA
Ecosystem	NA
Year added	2024
Last update	2024
status	incomplete
Version	000.001
Version comment	First draft
url	https://github.com/NINAnor/ecRxiv

Pollinator potential indicators

1. Introduction

2. About the underlying data

2.1 Spatial and temporal resolution

2.2 Original units

2.3 Additional comments about the dataset

3. Indicator properties

3.1. ECT

3.2. Ecosystem condition characteristic

3.3. Other standards

3.4. Collinearities with other indicators

4. Reference condition and values

4. 1. Reference condition

4. 2. Reference values

4.2.1 Minimum and maximum values

4.2.2. Threshold value for defining good ecological condition (if relevant)

4.2.3. Spatial resolution and validity

5. Uncertainties

6. References

7. Datasets

7.1 Pollinator datasets

7.2. Plant datasets

7.3. Covariates

8. Spatial units

9. Analyses

9.1. General overview of ISDMs

9.2. ISDM for pollinators

9.2.1 Priors

9.2.2 Fit model and make predictions

9.2.3 Pollinator ISDM validation

9.3. ISDM for plant species

9.3.1 Priors

9.3.2 Model fitting and predictions

9.4 Species Interractions

9.5. Diversity Indices

10. Results

10.1. Distribution of pollinators accross Norway

11. Export file

12. References